Christadelphian congregations are autonomous; there is no world-wide structure overseeing them all. On one end of the spectrum there are ecclesias who practice an open table, or as it is called, a "grace table", whereby any can partake of the bread and wine, whether or not they are members or baptized; some permit children to take of the emblems. On the other end of the spectrum there are a number of congregations bearing the name Christadelphian who consider that all other Christadelphians are apostate, and only they hold the true faith. They will not fellowship in any sense with other Christadelphians or Christian groups.
The open table view of fellowship is growing in popularity within Christadelphia; the idea being that all are welcome, but the teaching remains in the hands of elders who uphold sound doctrine. Divisions over fellowship issues have divided the Christadelphian body and paralyzed it in many ways and areas; many are realizing the damage this has done, whilst others insist upon maintaining separation from all who think differently to them on any point lest the purity of doctrine be lost. The founder of the Christadelphians, John Thomas, advocated an open table, not considering participation at the breaking of bread to be a "test of fellowship". Later Christadelphian leaders disagreed with him on this point, but now there is a return to Christadelphian roots in this area.
The open table view is explained here. The traumas associated with the closed table view and the practice of disfellowship by Christadelphians are developed in the novel The Seventh Woman .
A positive Biblical view of what fellowship looks like in practice amongst Christadelphians can be found here. Other material includes: 7-6 Christadelphian Divisions | 7-6-1 Who Is My Brother? | 7-6-1-1 Guilt By Association | 7.6.2 Self Baptism | 7-6-3 The Atonement And Fellowship | 7-7 Are Christadelphians The Only Ones Who Have Truth? |
Video and audio: Fellowship and Baptism [1] Audio here | Fellowship and Baptism [2] Audio here | Christadelphian History and Current Issues Audio here | What knowledge is required before baptism? Are baptismal interviews necessary? |